Answer:
x = 1, 5
Step-by-step explanation:
f(g(x)) = 2(x^2+2)-3
= 2x^2+4-3
= 2x^2+1
g(f(x)) = (2x-3)^2+2
= 4x^2-12x+9+2
= 4x^2-12x+11
f(g(x)) = g(f(x))
2x^2+1 = 4x^2-12x+11
2x^2 = 4x^2-12x+11-1
2x^2 = 4x^2-12x+10
x^2 = (4x^2-12x+10)/2
x^2 = 2x^2-6x+5
x^2-2x^2 = -6x+5
-x^2 = -6x+5
x^2+6x-5 = 0
(x-1)(x-5) = 0
x-1 = 0 or x-5 = 0
x = 1 or x = 5
